Complexity, Applied Nonlinear Science and Metamaterials

Our research draws on universal concepts in nonlinear wave physics and applies them in a variety of technological materials-modelling contexts, including laser optics and electromagnetics, fluid dynamics, and solid mechanics.

Particular strengths include the analysis of spontaneous simple patterns (spatial structures with a single characteristic size, such as hexagons, honeycombs, squares, stripes, and spots), fractals (patterns possessing proportional levels of detail across many decades of scale), vortices, solitons (self-stabilizing waves that may be localized in space, time, or both), and chaotic dynamics. Theoretical analyses of nonlinear wave phenomena are routinely complemented by simulations on various high-performance computing facilities.

Our optics research involves modelling new regimes of light generation, using intrinsic nonlinear dynamics of laser-material interactions in driven cavities as a means of generating spontaneous fractal light for a range of applications. We are also interested in the propagation of spatial solitons (beams of laser light that self-collimate in a nonlinear medium) in new angular geometries, and the way in which such localized waves refract, scatter, and travel along at material boundaries. More recently, we have begun to consider novel spatial dispersion effects (important for a wide class of materials) and how they influence the propagation of nonlinear light pulses in optical waveguides.

Salford is also global leader in developing new applications for metamaterials – artificial materials not otherwise found in nature, and which exhibit a plethora of surprising and often counterintuitive properties. Potential applications involve spatial cloaks (which may be used to make objects invisible in particular frequency ranges, e.g., over the microwave band) and their more exotic space-time counterparts (or “history editors”, which can be used to cloak events in space-time), acoustic metamaterials, and novel developments involving antennae systems.

Highlights in our fluid dynamics research include the pioneering of new models, based on the Oseen approximation, to predict how vortices trailing behind an inflight aircraft behave. An understanding such phenomena is pivotal, for example, in establishing safe separation distances for the ‘super’ class of aircraft such as the Airbus A380. Recent advances have also been made in slender-body theory, which well-describes many applied problems including the motion and stability of missiles, ships, and submarines.

Our research on solid mechanics has historically focused primarily on solving mathematical problems involving elastic waves travelling in pre-stressed media, their constitutive and dispersion relations, and the role played by non-classical boundary conditions. This work has helped understand the propagation of waves in thin and deformed structures, which is a key factor in a broad range of engineering-materials applications.